Factual error: The contract Stone and his team force Carlton Wood and Harry Fielding to sign guaranteeing Fowler's widow the royalties from his invention for life is signed under duress and is therefore invalid. It is hard to believe that none of Stone's team don't know this, but it is impossible to believe that Carlton Wood wouldn't.
Factual error: In a number of episodes people are shown eating and drinking in the laboratories. For instance, in "Miss Willows' Regrets" Nick and Greg are seen eating fried chicken in the lab, and in "Overload" Sara eats a sandwich while watching Grissom experiment with her deli pickle. There are other examples. No reputable laboratory (which this is supposed to be) would allow its staff to eat or drink while in the lab. It is basic scientific protocol to prevent contamination of samples or the person picking up toxins on their food.
Factual error: When Monk visits the prison for the first time, he is searched, passed, and has a mini-panic attack because people have touched him. Sharona steps forward to comfort him, and she puts her arms around him. This is a very serious breach of procedure and it is not possible for the guards to miss it, because Sharona has not been searched. It's a common technique for trying to pass contraband called 'a touch through' - a person with an item to be smuggled into the prison (drugs, usually), passes them on to a person who has been searched and is therefore 'clean'. Monk would be taken back to the guard's station to be searched again. He would not be allowed leniency because the guards happen to know or to like him - visitor ingress and egress is always done under CCTV and the guard would know he was being watched - quite possibly by someone who doesn't know who Monk and Sharona are.
Factual error: Ryan, the laboratory technician, eats his lunch of burger and fries while discussing a murder case with Assistant D.A. Claire Kincaid. Trouble is, they are in his laboratory. No lab technician ever, ever eats or drinks in a laboratory - it is the most basic lab protocol imaginable. He could contaminate his samples in any one of a hundred ways, he inevitably contaminates his gloves or fingers with residue from his meal and he risks poisoning himself with accidental transfer. This is not a character error - lab security is hammered into science students starting with the first day of first year and number one on the list is never, ever eat or drink in your lab.
Factual error: When House is looking over his whiteboard of symptoms for the swimming patient, the symptom "Intercranial Hemorrhage" is shown on the board. However, this is an error. The correct term is "Intracranial Hemorrhage." Anything inside the head is referred to as "intra" not "inter." This is a common mistake for laypeople, however the highly trained and knowledgeable Dr. House should not have made that error. (00:31:25)
Factual error: The naval captain in this episode has a military mustache as prescribed by army regulations. The Royal Navy regulations, however, prohibited separate mustaches and beards - if facial hair was worn, a "full set" of beard and mustache with the beard joined to the mustache was mandatory, and that to be grown to the commanding officer's satisfaction within six weeks.
Factual error: A thief has stolen 75 million dollars. He runs out with two large duffel bags. All US bills weigh a single gram. This means that $1,000,000 in $100 bills - the largest bills in circulation - weigh around 10 kilograms, or a little over 22 pounds. $75 million would be 1,650 pounds. No way this could be carried in two duffel bags.
Factual error: Calleigh Duquesne frequently wears completely inappropriate clothing throughout the whole series. She often wears blouses that are so low cut that the neckline is below the lower curve of her breasts. No officer of the court in the US would be allowed to dress this way. There is no grey area here, and this is not a character mistake - first time a CSI turned up at work dressed like that, she'd be sent home to change. Second time, she'd be on suspension until she agreed to change her dress standards. Also (and this regularly happens in CSI: NY as well) she is regularly wearing high heels - also a certain no-no for as CSI. Incidentally, male CSIs have equally strict dress standards.
Factual error: In the whole episode, Romania is depicted as a monarchy with the king in a position that allows him to make political decisions. However, Romania ceased to be a monarchy in 1947. By the time depicted in the episode (circa 1997), Romania was a republic and its head of state was the president. Members of the ex-royal family did not hold any positions in the Romanian government and were certainly not authorized to represent Romania in international events.